Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems II: Full Counting Statistics

TL;DR

This paper explores how topological invariants in the counting statistics of Markovian stochastic systems lead to quantized currents at low temperatures, extending the understanding of robust quantization phenomena.

Contribution

It introduces a topological classification framework for counting statistics in driven stochastic systems, linking quantized currents to topological invariants.

Findings

Quantized currents are linked to topological invariants.

Quantization persists at finite temperatures under certain conditions.

Provides a classification scheme for topological properties of counting statistics.

Abstract

We study Markovian stochastic motion on a graph with finite number of nodes and adiabatically periodically driven transition rates. We show that, under general conditions, the quantized currents that appear at low temperatures are a manifestation of topological invariants in the counting statistics of currents. This observation provides an approach for classification of topological properties of the counting statistics, as well as for extensions of the phenomenon of the robust quantization of currents at low temperatures to the properties of the counting statistics which persist to finite temperatures.